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Theorem sucex 6646
Description: The successor of a set is a set. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
sucex.1
Assertion
Ref Expression
sucex

Proof of Theorem sucex
StepHypRef Expression
1 sucex.1 . 2
2 sucexg 6645 . 2
31, 2ax-mp 5 1
Colors of variables: wff setvar class
Syntax hints:  e.wcel 1818   cvv 3109  succsuc 4885
This theorem is referenced by:  orduninsuc  6678  tfindsg  6695  tfinds2  6698  finds  6726  findsg  6727  finds2  6728  seqomlem1  7134  oasuc  7193  onasuc  7197  infensuc  7715  phplem4  7719  php  7721  inf0  8059  inf3lem1  8066  dfom3  8085  cantnflt  8112  cantnflem1  8129  cantnfltOLD  8142  cantnflem1OLD  8152  cnfcom  8165  cnfcomOLD  8173  infxpenlem  8412  pwsdompw  8605  ackbij1lem5  8625  cfslb2n  8669  cfsmolem  8671  fin1a2lem12  8812  axdc4lem  8856  alephreg  8978  dfon2lem7  29221  dford3lem2  30969  bnj986  34012  bnj1018  34020  bj-1ex  34507  bj-2ex  34508
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691  ax-un 6592
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-rex 2813  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-sn 4030  df-pr 4032  df-uni 4250  df-suc 4889
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